Truly nonparametric change point tests do not have obvious connections
to the canonical mean change detection problem.
These tests often involve appropriately weighted integrals over
differences of the estimators of the nonparametric quantity of interest,
such as those based on
functionals of two-sample rank-based tests [1]},
empirical characteristic function [2]},
and the tests for changes in a regression function based
on kernel estimators [3]} among others.
In principle, local testing-based methodologies for the canonical data segmentation problem
such as WBS or the MOSUM procedure, can be adapted to such tests,
since they are based on localised applications of tests designed for the AMOC setting.
On the other hand, application of the global optimisation approaches to nonparametric settings is more involved, although some attempts exist [4]}.
